dd ee zz riri oo hh utut AA e e rr uu ss oo clcl ss On the Utility Consistency of Poverty Lines DiDi c c blibli uu 1 PP Martin Ravallion and Michael Lokshin Development Research Group, World Bank, 1818 H Street NW, Washington DC, USA dd ee zz riri oo hh utut AA e e Abstract: Although poverty lines are widely used as deflators for inter-group rr uu ss oo welfare comparisons, their internal consistency is rarely given close scrutiny. A clcl ss DiDi priori considerations suggest that commonly used methods cannot be relied upon c c blibli uu to yield poverty lines that are consistent in terms of utility, or for capabilities PP more generally. The theory of revealed preference offers testable implications of utility consistency for “poverty baskets” under given preferences. A case study of dd ee zz riri Russia’s official poverty lines reveals numerous violations of revealed preference oo hh utut criteria — violations that are not solely attributable to heterogeneity in AA e e urur preferences associated with climatic differences. ss oo clcl ss DiDi c c JEL: D12, I32, R13 blibli uu PP Keywords: Poverty lines, revealed preference, capabilities, nutrition, Russia World Bank Policy Research Working Paper 3157, October 2003 dd ee zz riri The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange oo hh of ideas about development issues. An objective of the series is to get the findings out quickly, even if the utut AA presentations are less than fully polished. The papers carry the names of the authors and should be cited e e accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. rr uu ss They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they oo clcl represent. Policy Research Working Papers are available online at http://econ.worldbank.org. ss DiDi c c blibli uu PP 1 For comments the authors are grateful to Stefan Klonner and participants at the 2003 Cornell University Conference of “Poverty, Inequality and Development” in honor of Erik Thorbecke. These are the views of the authors, and need not reflect those of the World Bank or any affiliated organization. Correspondence: [email protected], [email protected]. 1. Introduction Poverty profiles — showing how a measure of poverty varies across sub-groups of a population — are widely used to inform policies for fighting poverty. A key ingredient is a set of poverty lines, to be used as deflators applied to sub-group specific distributions of income. Various methods are found in practice for setting poverty lines and the methodological choices made can matter greatly to the policy implications drawn. For example, a case study for Indonesia found virtually zero rank correlation between the regional poverty measures implied by two common methods of setting poverty lines (Ravallion and Bidani, 1994). This suggests that it is important to probe critically into the methods used to set poverty lines in practice. In identifying principles for choosing between alternative methods, the most obvious criterion for an economist is utility consistency, meaning that the poverty line for each sub-group is the cost of a common (inter-personally comparable) utility level across all sub-groups. This paper explores the implications of utility consistency for applied work. Poverty lines are usually anchored to nutritional requirements for good health and normal activities. But there are many ways this can be done. There are two common methods of setting poverty lines in practice: the “Food-Energy Intake” (FEI) method and the “Cost-of-Basic Needs” (CBN) method.2 The FEI method finds the income or expenditure level at which pre-determined food- energy requirements are met in expectation within each sub-group. There is no explicit bundle of goods in the FEI method. The CBN method, by contrast, sets specific poverty bundles and costs them in each sub-group. The food bundles are typically anchored to nutritional 2 For an overview of alternative methods found in practice see Ravallion (1998). Note that we refer here to commonly used “objective” poverty lines. Subjective poverty lines can also be defined and measured and we believe that this approach has a number of attractions, as discussed in (inter alia) Kapteyn et al., (1988) and Pradhan and Ravallion (2000). 2 requirements given prevailing diets, but allowances for non-food goods and services are also included. The paper argues that FEI poverty lines are unlikely to be utility consistent. CBN poverty lines are potentially utility consistent, but whether they are in practice is unclear. We explore one way of assessing the utility consistency of CBN poverty lines, based on longstanding ideas on the use of quantity indices in comparing alternative price and quantity combinations, invoking Samuelson’s (1938) theory of revealed preference.3 This yields testable necessary conditions for utility consistency for given preferences over commodities. As a case study, we apply these ideas to an assessment of Russia’s official poverty lines, which use an elaborate version of the CBN method. Russia’s striking climatic differences across regions mean that the same consumption bundle is unlikely to yield the same utility. (Large regions of Russia have average annual temperatures well below freezing, while other regions have moderate northern-European climates.) By implication, CBN poverty lines should have higher value (assessed by a quantity index) in colder climates. That is what we find in the data. However, we also find differences within similar climatic regions, and numerous violations of revealed preference criteria. Section 2 discusses alternative theoretical foundations for defining the consistency of poverty lines. Section 3 then focuses on FEI poverty lines. Section 4 turns to CBN poverty lines, while section 5 develops our revealed-preference tests for their utility consistency. We then carry the results of section 5 to our assessment of Russia’s official poverty lines; section 6 describes our data, while section 7 presents our results. Conclusions can be found in section 8. 3 For excellent overviews of the theory see Sen (1979) and Deaton and Muellbauer (1980, section 2.6 on revealed preference theory; also see section 7.2 on quantity indices). 3 2. Consistency of poverty lines in theory A poverty line can be defined as the money needed to achieve the minimum level of “well-being” that is required to not be deemed “poor.” Thus everyone at the poverty line (no matter what sub-group they happen to belong) is deemed to be equally badly off, and all those below the line are worse off than all those above it. This much can be easily agreed. The more difficult question is what concept of well-being should serve as the anchor for poverty lines? For economists the obvious answer is “utility.” A justification for utility consistent poverty lines can be found by applying standard welfare-economic principles to poverty measurement. These principles are that assessments of social welfare (including poverty measures) should depend solely on utilities, people with the same initial utility should be treated the same way, and social welfare should not be decreasing in any utility. To formalize this approach to setting poverty lines, consider household i in sub-group j with characteristics x (a vector).4 The household’s preferences are represented by an ij interpersonally comparable utility function u (q ,x ). The household chooses its consumption j ij ij vector q to maximize utility. Notice that we allow the possibility that the same commodity ij bundle can yield different utility levels in different subgroups for households with the same characteristics. For example, a given bundle may yield a higher utility in a warm climate than a cold one, where more will be needed for clothing and energy. The utility-consistent poverty line is the point on the consumer’s expenditure function corresponding to a common reference utility level and prevailing prices. The consumer’s expenditure function is e (p ,x ,u), giving the minimum cost of utility u in sub-group j when j ij ij 4 Ideally this would be the characteristics of individual rather than households. That is an important distinction, but not one that is implementable with the data normally available for measuring poverty. 4 facing the price vector p with household characteristics x . Let u denote the minimum ij ij z utility level deemed to be needed to escape poverty; consistency requires that this is a constant. The money metric of u defines a set of utility-consistent poverty lines: z zu =e (p ,x ,u ) for all (i, j) (1) ij j ij ij z When expenditure is deflated by such a poverty line one obtains a welfare metric with a number of desirable theoretical properties for policy analysis (Blackorby and Donaldson, 1987).5 For economists, utility is the obvious anchor for setting poverty lines. However, it is not the only possible approach, and nor is it the approach that has had most influence on practices in applied work on poverty (as we will show in the following sections). Capability-based concepts of well-being offer an alternative theoretical foundation for poverty measurement. Indeed, this can be viewed as an encompassing framework, for which utility consistency is a special case. While versions of this approach go back a long way in philosophy and the social sciences, it can be characterized today in the terms of Amartya Sen’s argument that “well-being” should be thought of in terms of a person’s capabilities, i.e., the functionings (“beings and doings”) that a person is able to achieve (Sen, 1985). By this view, poverty means not having an income sufficient to support specific normative functionings. Utility — as the attainment of personal satisfaction —can be viewed as one such functioning relevant to well-being (Sen, 1992, Chapter 3). But it is only one of the functionings that matter. Independently of utility, one might say that a person is better off if she is able to participate fully in social and economic activity, for example. Notice that poverty is not defined by actual achievement of these functionings, but rather by the capability of achieving them. 5 Such poverty lines can also be used to construct true cost-of-living indices, by normalizing the poverty line by its value for some reference group (see, for example, Deaton and Muellbauer, 1980). 5 To formalize this approach, let a household’s functionings be determined by the goods it consumes and its characteristics. The vector of actual functionings for household i in group j is: f = f (q ,x ) (2) ij j ij ij where f is a vector-valued function. The quantities consumed are assumed to be utility maximizing, giving demand functions q = q (p ,y ,x ) at total expenditure y . One can ij j ij ij ij ij also postulate that the household has preferences over functionings, for which u (q ,x ) is then j ij ij a derived utility function, obtained by substituting (2) into the (primal) utility function defined over functionings (Ravallion, 1998). Capability-consistency requires that certain normative funtionings are reached at the poverty line in each sub-group. Let f denote the vector of critical functionings deemed to be z needed to be not poor. (These are normative judgments, just as u is a normative judgment.) A z commodity bundle, qc, is identified such that no functioning is below its critical value: ij f ≤ f (qc,x ) (3) z j ij i There could well be more than one solution for qc satisfying (3). Each solution yields a ij set of capability-consistent poverty lines zc = p qc when qc is valued at local prices. Two ij ij ij ij ways can be suggested for choosing a single capability-consistent poverty line for each sub- group. The first possible way to resolve the indeterminacy of multiple solutions is to pick the bundle that minimizes the expenditure p qc over the set of all qc satisfying (3). Or one can ij ij ij define zc as the minimum y such that: ij f ≤ f [q (p ,y,x ),x ] (4) z j j ij ij ij 6 Notice that one or more specific functionings will be decisive in determining zc, namely the ij functioning that is the last to reach its critical value as income rises. In this sense, the lowest priority functioning for the household given its preferences over functionings will be decisive. A second possible approach is to treat attainments as a random variable (i.e., with a probability distribution) and take a mean conditional on income and other identified covariates, including group membership. Then poverty lines are deemed to be capability consistent if f is z reached in expectation. This second approach is closer to current practices for an important class of methods for setting poverty lines, which we turn to in the next section. 3. The food-energy-intake method The FEI method can be interpreted as a special case of the capability-based approach described above. The specialization is to focus on just one functioning, namely food-energy intake. The method finds the consumption expenditure or income level at which food energy intake is just sufficient to meet pre-determined food energy requirements for good health and normal activity levels. (Such caloric requirements are given in WHO, 1985, for example.) To deal with the fact that food energy intakes naturally vary at a given income level, the FEI method typically calculates an expected value of intake at given income. Figure 1 illustrates the method. The vertical axis is food-energy intake, plotted against income (or expenditure) on the horizontal axis. A line of “best fit” is indicated; this is the expected value of caloric intake at given income (i.e., the nonlinear regression function). By simply inverting this line, one finds the income z at which a person typically attains the stipulated food-energy requirement.6 This method, or 6 Some versions of the FEI method regress (or graph) nutritional intake against consumption expenditure and invert the estimated function, while others avoid this step by simply regressing 7 something similar, has been used often, including by Dandekar and Rath (1971), Osmani (1982), Greer and Thorbecke (1986), Paul (1989), Palmer-Jones and Sen (2001), and by numerous governmental statistics offices. It is probably the most common method found in practice in developing countries. To explain the method more formally, let k denote food-energy intake, which is taken to be a random variable. The stipulated requirement level is kr which is taken to be fixed for given characteristics, such as age. As long as the expected value of food-energy intake conditional on total consumption expenditure, E(k y), is strictly increasing in y over an interval that includes kr there will exist a FEI poverty line, zFEI , defined implicitly by: E(k zFEI) = kr (5) Three points are notable. Firstly, the method is aiming to measure income poverty, rather than undernutrition. If one wanted to measure undernutrition, one would simply look at how many people had nutritional intakes k ≤kr , ignoring incomes or consumption expenditures. Secondly, the method is computationally simple. A common practice is to calculate the mean income or expenditure of a sub-sample of households whose estimated caloric intakes are approximately equal to the stipulated requirements. More sophisticated versions use regressions of the empirical relationship between food energy intakes and consumption expenditure. These can be readily used (numerically or explicitly) to calculate the FEI poverty line. The method avoids the need for price data; in fact, no explicit valuations are required. Thirdly, the method automatically includes non-food consumption as long as one locates the total consumption expenditure at which a person typically attains the caloric requirement. consumption expenditure on nutritional intake. These two methods need not give the same answer, though the difference is not germane to our present interest; either way the following points apply. 8 Can the FEI method assure that the resulting poverty lines will be consistent in terms of utility or capabilities more generally? To assess their utility consistency, consider first how FEI poverty lines respond to differences in relative prices, which can of course differ across the sub- groups (such as regions) being compared in the poverty profile and over time. For example, the prices of many non-food goods are likely to be lower relative to foods in urban than in rural areas. This will probably mean that the demand for food and (hence) food energy intake will be lower in urban than in rural areas, at any given real income. But this does not, of course, mean that urban households are poorer at a given expenditure level. To see the problem more clearly, let there be two composite goods, “food” and “non- food” consumed in quantities q and q respectively, and let p denote the relative price of the 0 1 non-food good. The utility-consistent poverty line is (simplifying notation) zu = e(p,u ). By z the envelope property, the derivative of z w.r.t p is simply the level of consumption of non-food goods for someone at the poverty line. As long as both goods are consumed, a higher relative price of non-food goods must mean a higher poverty line in terms of food. However, this no longer holds using the FEI method to set the poverty line. Then one fixes instead the value of q at the (unique) level needed to achieve the stipulated food-energy 0 level. The corresponding FEI poverty line is zFEI such that q (p,zFEI) is the required food 0 consumption, where q (p,y) denotes the food demand function. The derivative of the FEI 0 poverty line w.r.t. the price of non-food goods is now: ∂zFEI q (p,zFEI) 0p = − (6) ∂p q (p,zFEI) 0y 9 where the subscripts “p” and “y” denote the partial derivatives w.r.t. those variables. It is reasonable to assume that non-food goods are normal (q > 0). The sign of (6) will then depend 0y on whether food and non-food goods are (uncompensated) substitutes (q > 0) or complements 0p (q < 0). In the former case, the FEI poverty line will decrease with an increase in the price of 0p non-food goods. A lower relative price of non-food goods in urban areas, for example, will perversely yield a higher poverty line using this method. The FEI poverty lines will then fail our consistency requirement since the consistent poverty lines must be increasing in all prices, given that this must hold for the consumer’s expenditure function. Utility consistency would requite that food and non-food goods are complements. There are other reasons to question the utility consistency of FEI poverty lines. Even if relative prices do not differ, the relationship between food energy intake and income will shift according to differences in tastes, activity levels and publicly-provided goods. There is nothing in the FEI method to guarantee that these differences are ones that would normally be considered relevant to assessing welfare. For example, tastes can differ across sub-groups even if relative prices do not. At given relative prices and real total expenditure, urban households may simply have more expensive food tastes than rural households; they eat more animal protein and less calories from starchy food staples, or simply eat out more often. Thus they pay more for each calorie, or (equivalently) food energy intake will be lower at any given real expenditure level. It is unclear why we would deem a person who chooses to buy fewer and more expensive calories as poorer than another person at the same real expenditure level. For these reasons, the real income at which an urban resident typically attains any given caloric requirement will tend to be higher than in rural areas. And this can hold even if the cost of living is no different between urban and rural areas. 10